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We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newtons gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in thecompact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications.
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Perhaps the greatest challenge for fundamental theories based on compactification from extra dimensions is accommodating a period of accelerated cosmological expansion. Previous studies have identified constraints imposed by the existence of dark energy for two overlapping classes of compactified theories: (1) those in which the higher dimensional picture satisfies certain metric properties selected to reproduce known low energy phenomenology; or (2) those derived from string theory assuming they satisfy the Swampland conjectures. For either class, the analyses showed that dark energy is only possible if it takes the form of quintessence. In this paper, we explore the consequences for theories that belong to both classes and show that the joint constraints are highly restrictive, leaving few options.
We discuss a realization of a small field inflation based on string inspired supergravities. In theories accompanying extra dimensions, compactification of them with small radii is required for realistic situations. Since the extra dimension can have a periodicity, there will appear (quasi-)periodic functions under transformations of moduli of the extra dimensions in low energy scales. Such a periodic property can lead to a UV completion of so-called multi-natural inflation model where inflaton potential consists of a sum of multiple sinusoidal functions with a decay constant smaller than the Planck scale. As an illustration, we construct a SUSY breaking model, and then show that such an inflaton potential can be generated by a sum of world sheet instantons in intersecting brane models on extra dimensions containing $T^2/{mathbb Z}_2$ orbifold. We show also predictions of cosmic observables by numerical analyzes.
We study the possibility that dark energy is a manifestation of the Casimir energy on extra dimensions with the topology of $S^2$. We consider our universe to be $M^4 times S^2$ and modify the geometry by introducing noncommutativity on the extra dimensions only, i.e. replacing $S^2$ with the fuzzy version $S_{F}^2$. We find the energy density as a function of the size of the representation $M+1$ of the algebra of $S_{F}^2$, and we calculate its value for the $M+1=2$ case. The value of the energy density turns out to be positive, i.e. provides dark energy, and the size of the extra dimensions agrees with the experimental limit. We also recover the correct commutative limit as the noncommutative parameter goes to zero.
In this paper we study the general scenario of an effective theory coming from the compactification of a higher dimensional theory in a string inspired setting. This leads to gauge coupling unification at an intermediate mass scale. After having computed all the threshold corrections (due to Kaluza-Klein modes) to the running of the couplings of the MSSM we embark in a detailed phenomenological analysis of the model, based on the numerical package DarkSUSY, to find constraints on the scenario from Dark Matter data. The mass spectrum of the theory does not have tachyons. Moreover we find that the neutralino is still the LSP with a relic density compatible with the most recent experimental data. With respect to the standard mSUGRA scenario we find that the neutralino is higgsino like in most of the parameter space. Our modifications to the DarkSUSY package will be shortly available upon request.
The holographic principle asserts that the entropy of a system cannot exceed its boundary area in Planck units. However, conventional quantum field theory fails to describe such systems. In this Letter, we assume the existence of large $n$ extra dimensions and propose a relationship between UV and IR cutoffs in this case. We find that if $n=2$, this effective field theory could be a good description of holographic systems. If these extra dimensions are detected in future experiments, it will help to prove the validity of the holographic principle. We also discuss implications for the cosmological constant problem.
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